Theme Essential Question: How can you apply and extend the usage of rational numbers when dealing with real world problems?
Essential Questions:
How do you compare rational numbers in fraction and decimal form?
How do you convert a rational number between fraction and decimal form?
Standards: 7. NS.2: Apply and extend previous understandings of multiplication and division and of fractions to multiply, and divide rational numbers.
7. NS.2d: Convert a rational number to a decimal using long division; know that the decimal form of a rational number terminates in 0s or eventually repeats.
Objectives: Prior knowledge and its extension:
The student will compare rational numbers (fractions and/or decimals) using the greater than, less than, or equal to symbols. The students will extend this knowledge to include negative rational numbers.
The student will graph rational numbers on the number line. The students will extend this knowledge to include negative rational numbers.
The student will add and subtraction fractions (positive numbers only)
The student will use long division to convert rational numbers to their equivalent decimal form.
The student will recognize rational numbers and its representation as a repeating or terminating decimal.
Reflections and/or Comments from your PCSSD 7th Grade Curriculum Team It is recommended, in order to facilitate the next lesson, that review and practice be provided on the 6th grade skill of adding and subtraction fractions, positive numbers only.
Background Information Recommended: For a quick overview of the standard(s) to be addressed in this lesson, see Arizona’s Content Standards Reference Materials at http://www.azed.gov/educator-certification/
Taken from Ohio Dept of Education Mathematics Model Curriculum 6-28-2011) In Grade 7 the awareness of rational and irrational numbers is initiated by observing the result of changing fractions to decimals. Students should be provided with families of fractions, such as, sevenths, ninths, thirds, etc. to convert to decimals using long division. The equivalents can be grouped and named (terminating or repeating). Students should begin to see why these patterns occur. Knowing the formal vocabulary rational and irrational is not expected.
Assessment: Product This will be an ongoing product that will be developed during each week of the unit. Continue foldables this week with long division.
Foldable
Make a foldable with five divided sections (3 pieces of paper needed). Students will create a section for each of the following:
Addition- Have written rule and examples using integers, fractions, and decimals.
Subtraction- Have written rule and examples using integers, fractions, and decimals.
Multiplication- Have written rule and examples using integers, fractions, and decimals.
Division- Have written rule and examples using integers, fractions, and decimals.
Long Division- Have written rule and examples.
Key Questions
How do you compare rational numbers in fraction and/or decimal form?
What is the process to change rational numbers between their fractional and decimal equivalent form?
When is a decimal not a rational number?
How do you know if a fraction has a repeating decimal? Terminating decimal?
Observable Student Behaviors
The student can compare rational numbers in fraction and/or decimal forms using numerical comparison techniques.
The student can plot rational numbers on a number line.
The student can convert rational numbers between fraction and decimal forms.
The student can explain that a rational number in decimal form terminates in 0s or eventually repeats.
Mathematical Practices 1. Make sense of problems and persevere in solving them. 2. Reason abstractly and quantitatively. 3. Construct viable arguments and critique the reasoning of others. 4. Model with mathematics. 5. Use appropriate tools strategically. 6. Attend to precision. 7. Look for and make use of structure. 8. Look for and express regularity in repeated reasoning.
Vocabulary:
Math
Rational Number Additive Inverse Decimals Fractions Integers Negative Numbers Number Line Opposites Positive Numbers
Suggested Activities: On Core Mathematics 1-1 pp. 3-6 Mastering the COMMON CORE in Mathematics Grade 7 by American Book Company, Review
Comparing Fractions 2.2 pp. 13
Comparing Decimals 2.3 pp. 14
Graphing Rational Numbers on a Number line 2.6 pp.18-19
Comparing Rational Numbers 2.7 pp.20
Changing Fractions to Decimals 2.4 -pp. 15-16
Practice Chapter 2 Review and Test. Pp 21-22
Teaching the Common Core Math Standards with Hands-On Activities
NS.1 p. 90
Highly Recommended
Nothing available at this time (NS.2)
The Illustrative Mathematics Project offers guidance to states, assessment consortia, testing companies, and curriculum developers by illustrating the range and types of mathematical work that students will experience in a faithful implementation of the Common Core State Standards. The website features a clickable version of the Common Core in mathematics and the first round of "illustrations" of specific standards with associated classroom tasks and solutions.
JBHM 7th Glencoe Mathematics Application and Concepts Course 2 5.4, pp. 210-213 Glencoe Pre-Algebra 5.1, pp. 200-204
Perry the Penguin needs 9 clams to buy an ice scooter -- but he's not very good at saving. As Perry earns, spends, finds, loses, and borrows clams, a simple line graph demonstrates the concept of negative numbers.
Many children's books include math concepts and can be used to help teach them in a fun way. This website includes several annotated Lists of Children's Literature including the math concepts and grade levels.
Lost in Lexicon: An Adventure in Words and Numbers by Pendred Noyce and Joan Charles (Jul 26, 2011)
"If this is an adventure, we should just plunge in..."
When thirteen-year-old cousins Ivan and Daphne go on a treasure hunt in the rain one summer day, they never expect to stumble into a whole new world where words and numbers run wild. After the cousins outwit a plague of punctuation, grateful villagers beg them to find Lexicon's missing children, who have been enticed away by dancing lights in the sky. Trekking between villages in search of clues, the cousins encounter a talking thesaurus, a fog of forgetting, the Mistress of Metaphor, a panel of poets, feuding parts of speech, and the illogical mathematicians of Irrationality. When a careless Mathemystical reflects them across the border into the ominous Land of Night, their peril deepens. Kidnapped, imprisoned, and mesmerized—with time running out—will Ivan and Daphne find a way to solve the mystery of the lights in the sky and restore the lost children of Lexicon to their homes?
Lost in Lexicon will whisk children away into an interactive and magical world of learning.
101 Things Everyone Should Know About Math by Marc Zev, Kevin Segal and Nathan Levy (Mar 16, 2010) (real world)
Math is a critical part of our everyday lives; we use it dozens of times daily and wish we understood it better. The second title in the 101 Things Everyone Should Know series, this book makes understanding math easy and fun! Using an appealing question and answer format, this book is perfect for kids, grown-ups and anyone interested in the difference between an Olympic event score of 9.0 and Richter scale score of 9.0.
The teaching Channel currently offers videos of K-12 mathematics teaching aligned with the Common Core Sate Standards, which would be perfect for professional development with teacher teams.
Interactivate is a set of free, online courseware for exploration in science and mathematics. It is comprised of activities, lessons, and discussions. The site is structured around collections of activities, lessons, and discussions.
Content: Rational Numbers - Fundamentals
Theme Essential Question:
How can you apply and extend the usage of rational numbers when dealing with real world problems?
Essential Questions:
Standards:
7. NS.2: Apply and extend previous understandings of multiplication and division and of fractions to multiply, and divide rational numbers.
Objectives:
Prior knowledge and its extension:
Reflections and/or Comments from your PCSSD 7th Grade Curriculum Team
It is recommended, in order to facilitate the next lesson, that review and practice be provided on the 6th grade skill of adding and subtraction fractions, positive numbers only.
Background Information
Recommended: For a quick overview of the standard(s) to be addressed in this lesson, see Arizona’s Content Standards Reference Materials at http://www.azed.gov/educator-certification/
Taken from Ohio Dept of Education Mathematics Model Curriculum 6-28-2011)
In Grade 7 the awareness of rational and irrational numbers is initiated by observing the result of changing fractions to decimals. Students should be provided with families of fractions, such as, sevenths, ninths, thirds, etc. to convert to decimals using long division. The equivalents can be grouped and named (terminating or repeating). Students should begin to see why these patterns occur. Knowing the formal vocabulary rational and irrational is not expected.
Assessment:
Product
This will be an ongoing product that will be developed during each week of the unit. Continue foldables this week with long division.
Key Questions
Observable Student Behaviors
1. Make sense of problems and persevere in solving them.
2. Reason abstractly and quantitatively.
3. Construct viable arguments and critique the reasoning of others.
4. Model with mathematics.
5. Use appropriate tools strategically.
6. Attend to precision.
7. Look for and make use of structure.
8. Look for and express regularity in repeated reasoning.
Vocabulary:
Fractions Integers Negative Numbers
Number Line Opposites Positive Numbers
Suggested Activities:
On Core Mathematics 1-1 pp. 3-6
Mastering the COMMON CORE in Mathematics Grade 7 by American Book Company,
Review
- Comparing Fractions 2.2 pp. 13
- Comparing Decimals 2.3 pp. 14
- Graphing Rational Numbers on a Number line 2.6 pp.18-19
- Comparing Rational Numbers 2.7 pp.20
- Changing Fractions to Decimals 2.4 -pp. 15-16
- Practice Chapter 2 Review and Test. Pp 21-22
Teaching the Common Core Math Standards with Hands-On Activities- NS.1 p. 90
Highly Recommended- Nothing available at this time (NS.2)
- The Illustrative Mathematics Project offers guidance to states, assessment consortia, testing companies, and curriculum developers by illustrating the range and types of mathematical work that students will experience in a faithful implementation of the Common Core State Standards. The website features a clickable version of the Common Core in mathematics and the first round of "illustrations" of specific standards with associated classroom tasks and solutions.
JBHM 7thGlencoe Mathematics Application and Concepts Course 2 5.4, pp. 210-213
Glencoe Pre-Algebra 5.1, pp. 200-204
Diverse Learners:
Homework:
Terminology for Teachers:
Ethnicity/Culture | Immigration/Migration | Intercultural Competence | Socialization | Racism/Discrimination
High Yield Strategies
Similarities/Differences | Summarizing/Notetaking | Reinforcing/Recognition | Homework/Practice |
Non-Linguistic representation | Cooperative Learning | Objectives/Feedback |
Generating-Testing Hypothesis | Cues, Questions, Organizers
Resources:
Professional Texts:
Literary Texts
Middle & High School: Literature in Mathematics
Informational Texts
Art, Music, and Media
Manipulatives
Games
Videos
- Discovery Learning
http://www.discoveryeducation.com/- The teaching Channel currently offers videos of K-12 mathematics teaching aligned with the Common Core Sate Standards, which would be perfect for professional development with teacher teams.
https://www.teachingchannel.org/videos?categories=topics common-coreSMART Board Lessons, Promethean Lessons
- Smart Board rational number lessons
http://exchange.smarttech.com/details.html?id=1764f052-3804-448f-9f12-95bc5646a2eaRational numbers Smart Board lessons
Other Activities, etc.
Language
Arts
Week 1
Week 2
Week 3
Week 4
Week 5
Week 6
7 Matrix
Accelerated 7
Matrix
Week 1
Week 2
Week 3
Week 4
Week 5
Week 6
Home K-2
Home 3-6
Home 6-8
Unit 1
Unit 2
Unit 3
Unit 4
Unit 5
Unit 6